Some new results for Dirichlet priors

Abstract

Let p be a random probability measure chosen by a Dirichlet process whose parameter a is a finite measure with support contained in $[0, +\infty)$ and suppose that $V = \int x^2p(dx)-[\int xp(dx)]^2$ is a (finite)random variable. This paper deals with the distribution of $V$, which is given in a rather general case. A simple application to Bayesian bootstrap is also illustrated.